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CVP reproduce

mechanical.beam.deflection

Independent re-run pack: fixed input vectors, O3 expected values, oracle version, commands, and the last result summary. This is how a reader moves from “CalculatorX says it passed” to “I can reproduce why it passed.”

Reproduce JSON CVP Manifest O3 table Generator REST checker Calculator

Identity

Calculation version, protocol version, and evidence revision are distinct.

Calculation version
1.0.0
CVP protocol
1.0.0-proposed · proposed
Evidence revision
2026-09-27.o2-o3.parent.iface.o3fix
Oracle
O3 · mpmath 1.4.1 · 80 dps
Generator
beam-deflection-contract-partitioned-o3 · seed 20260927.beam-deflection-o3
Table SHA-256
ac85afeb2106dd775e07c517629996243e2a59b8a3f2760d5e262c84a0bd27ac

Numerical claim

O3 PASS is a tabulated-vector claim, not a whole-domain proof.

O2: delta vs composed Layer-A separate-module identities (≤2 ULP). Multi-load is Σ δ_i. Not FEM, not indeterminate, not generic multi-load max. ≤2 ULP vs O3 applies only to tabulated Layer-A partitions projected from published leaf mpmath tables (simply_supported×point×midspan, cantilever×point×tip, simply_supported×uniform×midspan). Multi-load composition is out of O3 claim scope.

  • Last O3 run 24 / 24
  • Max error observed 1 ULP
  • Threshold ≤ 2 ULP

Commands

Regenerate the table from the public generator. Independent REST check needs only this page's reproduce.json plus stdlib Python — no repo clone and no mpmath. The CVP runner remains a maintainer command.

Regenerate O3 table
python3 generate-beam-deflection-o3.py after downloading the public generator next to the table
Repo maintainer path
python3 scripts/lib/cvp/oracles/generate-beam-deflection-o3.py
Independent REST check
Compare POST /api/v1/calc/mechanical-beam-deflection (contract shape) against partitioned leaf O3 tables under /developers/cvp/reproduce/ after downloading check-math-o3-rest.py next to beam-deflection-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP
npm run cvp:run -- --capability mechanical.beam.deflection
REST check
POST https://www.calculatorx.com/api/v1/calc/mechanical-beam-deflection with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 ac85afeb2106dd775e07c517629996243e2a59b8a3f2760d5e262c84a0bd27ac. Compare each expected_f64 to the production result within the declared ULP threshold.

Tabulated vectors

Every O3 vector used for the ≤2 ULP claim. Expected values come from the published mpmath table, not from the implementation under test.

IDKindInputsExpected (f64)ActualULPStatus
ss-point-midspan:o3-checkcheck{"support":"simply_supported","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":480}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":80,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":480}],"normalized_loads":[{"id":"P1","type":"point","P":480,"a":null}],"L":2,"E":1,"I":1,"x":1,"delta":80,"components":[{"id":"P1","delta":80,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-SISI{"support":"simply_supported","L":4,"E":200000000000,"I":0.00001,"loads":[{"id":"P1","type":"point","P":1000}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.0006666666666666665,"L":4,"E":200000000000,"I":0.00001}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":1000}],"normalized_loads":[{"id":"P1","type":"point","P":1000,"a":null}],"L":4,"E":200000000000,"I":0.00001,"x":2,"delta":0.0006666666666666665,"components":[{"id":"P1","delta":0.0006666666666666665,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-aliasalias{"support":"simply_supported","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":960}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":160,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":960}],"normalized_loads":[{"id":"P1","type":"point","P":960,"a":null}],"L":2,"E":1,"I":1,"x":1,"delta":160,"components":[{"id":"P1","delta":160,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-awkwardawkward{"support":"simply_supported","L":3.5,"E":210000,"I":0.83,"loads":[{"id":"P1","type":"point","P":137}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.0007020791499330656,"L":3.5,"E":210000,"I":0.83}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":137}],"normalized_loads":[{"id":"P1","type":"point","P":137,"a":null}],"L":3.5,"E":210000,"I":0.83,"x":1.75,"delta":0.0007020791499330656,"components":[{"id":"P1","delta":0.0007020791499330656,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-negsigned{"support":"simply_supported","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":-480}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":-80,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":-480}],"normalized_loads":[{"id":"P1","type":"point","P":-480,"a":null}],"L":2,"E":1,"I":1,"x":1,"delta":-80,"components":[{"id":"P1","delta":-80,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-smallsmall{"support":"simply_supported","L":1,"E":1000,"I":0.01,"loads":[{"id":"P1","type":"point","P":10}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.020833333333333332,"L":1,"E":1000,"I":0.01}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":10}],"normalized_loads":[{"id":"P1","type":"point","P":10,"a":null}],"L":1,"E":1000,"I":0.01,"x":0.5,"delta":0.020833333333333332,"components":[{"id":"P1","delta":0.020833333333333332,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-stiffstiff{"support":"simply_supported","L":3,"E":210000000000,"I":0.0002,"loads":[{"id":"P1","type":"point","P":5000}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.00006696428571428572,"L":3,"E":210000000000,"I":0.0002}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":5000}],"normalized_loads":[{"id":"P1","type":"point","P":5000,"a":null}],"L":3,"E":210000000000,"I":0.0002,"x":1.5,"delta":0.00006696428571428572,"components":[{"id":"P1","delta":0.00006696428571428572,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-point-midspan:o3-longlong{"support":"simply_supported","L":8,"E":70000000000,"I":0.00005,"loads":[{"id":"P1","type":"point","P":200}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.0006095238095238095,"L":8,"E":70000000000,"I":0.00005}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"P1","type":"point","P":200}],"normalized_loads":[{"id":"P1","type":"point","P":200,"a":null}],"L":8,"E":70000000000,"I":0.00005,"x":4,"delta":0.0006095238095238095,"components":[{"id":"P1","delta":0.0006095238095238095,"model":"offset_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-checkcheck{"support":"cantilever","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":3}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":8,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":3}],"normalized_loads":[{"id":"P1","type":"point","P":3,"a":null}],"L":2,"E":1,"I":1,"x":2,"delta":8,"components":[{"id":"P1","delta":8,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-SISI{"support":"cantilever","L":2,"E":200000000000,"I":0.00001,"loads":[{"id":"P1","type":"point","P":1000}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":0.001333333333333333,"L":2,"E":200000000000,"I":0.00001}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":1000}],"normalized_loads":[{"id":"P1","type":"point","P":1000,"a":null}],"L":2,"E":200000000000,"I":0.00001,"x":2,"delta":0.001333333333333333,"components":[{"id":"P1","delta":0.001333333333333333,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-aliasalias{"support":"cantilever","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":6}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":16,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":6}],"normalized_loads":[{"id":"P1","type":"point","P":6,"a":null}],"L":2,"E":1,"I":1,"x":2,"delta":16,"components":[{"id":"P1","delta":16,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-awkwardawkward{"support":"cantilever","L":3.5,"E":210000,"I":0.83,"loads":[{"id":"P1","type":"point","P":13.7}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":0.001123326639892905,"L":3.5,"E":210000,"I":0.83}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":13.7}],"normalized_loads":[{"id":"P1","type":"point","P":13.7,"a":null}],"L":3.5,"E":210000,"I":0.83,"x":3.5,"delta":0.0011233266398929047,"components":[{"id":"P1","delta":0.0011233266398929047,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}1PASS
cantilever-point-tip:o3-negsigned{"support":"cantilever","L":2,"E":1,"I":1,"loads":[{"id":"P1","type":"point","P":-3}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":-8,"L":2,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":-3}],"normalized_loads":[{"id":"P1","type":"point","P":-3,"a":null}],"L":2,"E":1,"I":1,"x":2,"delta":-8,"components":[{"id":"P1","delta":-8,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-smallsmall{"support":"cantilever","L":1,"E":1000,"I":0.01,"loads":[{"id":"P1","type":"point","P":10}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":0.3333333333333333,"L":1,"E":1000,"I":0.01}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":10}],"normalized_loads":[{"id":"P1","type":"point","P":10,"a":null}],"L":1,"E":1000,"I":0.01,"x":1,"delta":0.3333333333333333,"components":[{"id":"P1","delta":0.3333333333333333,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-stiffstiff{"support":"cantilever","L":1.5,"E":210000000000,"I":0.0002,"loads":[{"id":"P1","type":"point","P":500}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":0.000013392857142857142,"L":1.5,"E":210000000000,"I":0.0002}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":500}],"normalized_loads":[{"id":"P1","type":"point","P":500,"a":null}],"L":1.5,"E":210000000000,"I":0.0002,"x":1.5,"delta":0.000013392857142857142,"components":[{"id":"P1","delta":0.000013392857142857142,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
cantilever-point-tip:o3-longlong{"support":"cantilever","L":4,"E":70000000000,"I":0.00005,"loads":[{"id":"P1","type":"point","P":200}],"query":{"kind":"tip"}}{"oracle_layer":"analytic","delta":0.001219047619047619,"L":4,"E":70000000000,"I":0.00005}{"model":"mechanical.beam.deflection","support":"cantilever","query":{"kind":"tip"},"loads":[{"id":"P1","type":"point","P":200}],"normalized_loads":[{"id":"P1","type":"point","P":200,"a":null}],"L":4,"E":70000000000,"I":0.00005,"x":4,"delta":0.001219047619047619,"components":[{"id":"P1","delta":0.001219047619047619,"model":"cantilever_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-checkcheck{"support":"simply_supported","L":1,"E":1,"I":1,"loads":[{"id":"U1","type":"uniform","w":384}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":5,"L":1,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":384}],"normalized_loads":[{"id":"U1","type":"uniform","w":384}],"L":1,"E":1,"I":1,"x":0.5,"delta":5,"components":[{"id":"U1","delta":5,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-SISI{"support":"simply_supported","L":2,"E":200000000000,"I":0.00001,"loads":[{"id":"U1","type":"uniform","w":1000}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.00010416666666666665,"L":2,"E":200000000000,"I":0.00001}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":1000}],"normalized_loads":[{"id":"U1","type":"uniform","w":1000}],"L":2,"E":200000000000,"I":0.00001,"x":1,"delta":0.00010416666666666665,"components":[{"id":"U1","delta":0.00010416666666666665,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-aliasalias{"support":"simply_supported","L":1,"E":1,"I":1,"loads":[{"id":"U1","type":"uniform","w":768}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":10,"L":1,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":768}],"normalized_loads":[{"id":"U1","type":"uniform","w":768}],"L":1,"E":1,"I":1,"x":0.5,"delta":10,"components":[{"id":"U1","delta":10,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-awkwardawkward{"support":"simply_supported","L":3.5,"E":210000,"I":0.83,"loads":[{"id":"U1","type":"uniform","w":13.7}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.0001535798140478581,"L":3.5,"E":210000,"I":0.83}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":13.7}],"normalized_loads":[{"id":"U1","type":"uniform","w":13.7}],"L":3.5,"E":210000,"I":0.83,"x":1.75,"delta":0.00015357981404785808,"components":[{"id":"U1","delta":0.00015357981404785808,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}1PASS
ss-uniform-midspan:o3-negsigned{"support":"simply_supported","L":1,"E":1,"I":1,"loads":[{"id":"U1","type":"uniform","w":-384}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":-5,"L":1,"E":1,"I":1}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":-384}],"normalized_loads":[{"id":"U1","type":"uniform","w":-384}],"L":1,"E":1,"I":1,"x":0.5,"delta":-5,"components":[{"id":"U1","delta":-5,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-smallsmall{"support":"simply_supported","L":1,"E":1000,"I":0.01,"loads":[{"id":"U1","type":"uniform","w":10}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.013020833333333334,"L":1,"E":1000,"I":0.01}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":10}],"normalized_loads":[{"id":"U1","type":"uniform","w":10}],"L":1,"E":1000,"I":0.01,"x":0.5,"delta":0.013020833333333334,"components":[{"id":"U1","delta":0.013020833333333334,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-stiffstiff{"support":"simply_supported","L":1.5,"E":210000000000,"I":0.0002,"loads":[{"id":"U1","type":"uniform","w":500}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":7.847377232142857e-7,"L":1.5,"E":210000000000,"I":0.0002}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":500}],"normalized_loads":[{"id":"U1","type":"uniform","w":500}],"L":1.5,"E":210000000000,"I":0.0002,"x":0.75,"delta":7.847377232142857e-7,"components":[{"id":"U1","delta":7.847377232142857e-7,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS
ss-uniform-midspan:o3-longlong{"support":"simply_supported","L":4,"E":70000000000,"I":0.00005,"loads":[{"id":"U1","type":"uniform","w":200}],"query":{"kind":"midspan"}}{"oracle_layer":"analytic","delta":0.00019047619047619048,"L":4,"E":70000000000,"I":0.00005}{"model":"mechanical.beam.deflection","support":"simply_supported","query":{"kind":"midspan"},"loads":[{"id":"U1","type":"uniform","w":200}],"normalized_loads":[{"id":"U1","type":"uniform","w":200}],"L":4,"E":70000000000,"I":0.00005,"x":2,"delta":0.00019047619047619048,"components":[{"id":"U1","delta":0.00019047619047619048,"model":"uniform_load_at_deflection"}],"solver":"beam.deflection superposition of Layer-A At-curves","convention":"Euler–Bernoulli, constant EI, determinate supports. δ = Σ δ_i via existing statics-engine primitives."}0PASS